Parallel Manipulation and Flexible Assembly of Micro-Spiral via Optoelectronic Tweezers

Micro-spiral has a wide range of applications in smart materials, such as drug delivery, deformable materials, and micro-scale electronic devices by utilizing the manipulation of electric fields, magnetic fields, and flow fields. However, it is incredibly challenging to achieve a massively parallel manipulation of the micro-spiral to form a particular microstructure in these conventional methods. Here, a simple method is reported for assembling micro-spirals into various microstructures via optoelectronic tweezers (OETs), which can accurately manipulate the micro-/bio-particles by projecting light patterns. The manipulation force of micro-spiral is analyzed and simulated first by the finite element simulation. When the micro-spiral lies at the bottom of the microfluidic chip, it can be translated or rotated toward the target position by applying control forces simultaneously at multiple locations on the long axis of the micro-spiral. Through the OET manipulation, the length of the micro-spiral chain can reach 806.45 μm. Moreover, the different parallel manipulation modes are achieved by utilizing multiple light spots. The results show that the micro-spirulina can be manipulated by a real-time local light pattern and be flexibly assembled into design microstructures by OETs, such as a T-shape circuit, link lever, and micro-coil pairs of devices. This assembly method using OETs has promising potential in fabricating innovative materials and microdevices for practical engineering applications.

Generally, the spherical bioparticle is analyzed using the model called the multishell model (Jubery et al., 2014;Gagnon 2011;Qian et al., 2014), as shown in Supplement Figure 1A. Then, the multishell model can be equivalent to the double-shell model (as shown in Supplement Figure 1B) by a series of calculations. Finally, the double model also can be equivalent to a single-shell model (as shown in Supplement Figure 1C). Using the simplified single-shell sphere model, the effective complex permittivities( ) and conductivity of bioparticles(σ ) are expressed as (Jubery et al., 2014;Qian et al., 2014): where, 1 and 2 are the complex permittivity of the bioparticle membrane and cytoplasm, respectively. 1 and 2 are the radius of the outermost layer and inner layer of bioparticles, respectively. 1 and 2 are the complex permittivity of the bioparticle membrane and cytoplasm, respectively.
Here, because cell walls are permeable, we ignore the influence of the dielectric properties of cell walls in this model. We try to build an ideal equivalent single-shell spiral model for demonstrated moving characteristics, and eq. 1 and 2 are used to calculate the effective dielectric parameters in this simplified model. In addition, the spiral can be thought of as a lot of cylinders segments. According to the literature (Li et al., 2016;Tao et al., 2015;Dalir et al., 2009), the effective dielectric parameters could be used to analyze the property of the cylindrical shape. Thus, the CM factor is calculated by the effective complex permittivities and conductivity of the spiral. The preliminary simulation results show that the spiral is attracted by the light spot which agrees with the moving direction in the experiment. When the particle is a sphere, the dielectrophoresis force can be expressed as (Jubery et al., 2014;Gagnon 2011;Qian et al., 2014): Here, the spiral can be divided into a lot of cylinder segments. In order to simplify the calculation parameters, the depolarizing factor of three different axes is set to the same in any one cylinder segment. Therefore, the final model for calculation is approximately assumpted as the sphere.
In the OET system, the manipulation force can be calculated by Stokes's drag force (Zhang et al., 2019;Liang et al., 2020) which can be applied to measure the actual strength of DEP forces by the velocity of particles because the medium is laminar. Stokes's drag force is expressed as:

Supplementary Material
Here, in the moving direction, the spiral suffers a resistance force with a ring cross-section (the outer diameter and inner diameters are R and r respectively), as shown in Figure 5. The feature size of spirulina is 30μm in diameter (D), 6μm in wire diameter (d). Thus, R=D/2+d/2=18μm, r=R-d=12μm. The resistance area of the ring is calculated to A = ( 2 − 2 ) ≈ 3.14 × (18 2 − 12 2 ) × 10 −12 2 = 5.652 × 10 −10 2 . Then, we used the resistance area to calculate an equivalent circle diameter re (A = 2 ) for simplifying the calculation. re=1.342× 10 −5 m. The spirulina was moved at a maximum linear velocity of 4.57 μm/s. The kinematic viscosity of the medium, deionized water, is = 1 g/cm3. Therefore, according to Stokes's equation,

Supplementary Videos
Video clip 1: The MST simulation results and cooperatively manipulation of multiple light spots; Video clip 2: Parallel translated the micro-spirulina by multiple light spots in the OET system in the same direction and opposite direction; Video clip 3: Parallel rotated the micro-spirulina by multiple light spots in the OET system along with a point in the bottom electrode and a point of itself.
Video clip 4: Flexible assemble micro-spiral into the different shapes of micro-structure.